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The first half of Leviticus 15 revealed what the children of Israel had to do when a male had a bodily discharge, and the last half of the chapter deals with female discharges,

“If a woman has a discharge, and the discharge from her body is blood, she shall be set apart seven days; and whoever touches her shall be unclean until evening…And if any man lies with her at all, so that her impurity is on him, he shall be unclean seven days; and every bed on which he lies shall be unclean…But if she is cleansed of her discharge, then she shall count for herself seven days, and after that she shall be clean” (Leviticus 15.19, 24, 28).

Even as the cleansing ritual for the male required seven days, so it was for the female.

What did these things mean? Did this time of cleansing present some kind of symbol?

I do not know that the Bible reveals such, but we can continue to think that seven represents completion or perfection, just as it does here. When a woman went through the seven days of cleansing, she was totally clean after that time.